1. Field of the Invention
This invention relates to a process and apparatus for determination of permeability of porous media and thickness of layered porous media, such as underground formations, especially shaly formations having low permeability. Permeability may he determined according to this invention by measurement at a finite frequency of streaming potential and electro-osmotic induced pressure due to applied finite frequency pressure oscillations and alternating current, respectively, with use of both measurement coefficients in conjunction with electrical conductivity, which may be measured simultaneously or separately, to obtain the formation permeability. Permeability may also he obtained directly from measurement of the relaxation frequency of electro-osmosis coefficient alone. Thickness of layered porous materials, such as mudcake lining bore holes and layered porous rock, may be determined by measurement of streaming potential coefficient alone over a range of frequencies. In the apparatus of this invention, the differential pressure and voltage may be measured at substantially the point where pressure oscillations and sitemaring current are applied, that is, the distance between application and measurement electrodes is small compared to the sonic or subsonic wave length and the electrodes are removed from formation fluid flow paths. The apparatus may have a plurality of spaced measurement electrodes to provide measurement of the penetration depth of applied pressure oscillations for determination of thickness of layers of porous media and to largely remove the effect due to the mudcake in streaming potential measurements.
2. Description of Related Art
Several prior patents teach application of pulsed pressure and measurement of an a.c. signal of defined frequency in the measurement of streaming potential in a porous underground formation: U.S. Pat. No. 2,433,746 teaches vigorous vibration of a down hole apparatus to generate pressure oscillations for measurement, with one electrode down the borehole and the other at the surface, of the potential to ascertain the streaming potential; U.S. Pat. No. 2,550,005 teaches a modification of the method taught by the U.S. Pat. No. 2,433,746 patent by pressurizing the entire well to produce the periodic pulses in the borehole liquid; and U.S. Pat. No. 3,599,085 teaches use of a sonic transducer periodically exciting a formation at low frequencies to cause periodic electrokinetic potentials which are measured at a location near the transducer and at a location spaced from the transducer, the ratio of the measured potentials being related to the electrokinetic skin depth to provide an indication of permeability of the formation. U.S. Pat. No. 4,427,944 teaches application of pressure of alternating polarity to the formation and measurement of the generated transient streaming potentials in the time domain to estimate the characteristic response time which is inversely proportional to the formation permeability.
U.S. Pat. No. 4,864,845 teaches in-situ rock permeability measurements using an electronic field permeameter with a microcomputer which automatically turns on a gas supply, senses when a steady-state is reached, collects and records pressure and flow rate, and shuts off the gas supply immediately upon completion of the measurement. The injection pressure and flow rate of the gas is used to determine permeability.
U.S. Pat. No. 2,814,017 teaches measurement of the difference in phase between periodic pressure waves passed through a formation and potentials generated by the oscillatory motion of the formation caused by these pressure waves and, conversely, application of a periodically varying electric current to the formation fluid to generate periodic pressure waves in the formation by electro-osmosis. Measurements of the phase shift in the frequency domain between the generating and generated quantities is said to be a measure of permeability of the formation. U.S. Pat. No. 4,730,162 teaches time domain induced polarization with a square wave of alternating polarity being applied intermittently and alternately for induced polarization logging.
U.S. Pat. No. 3,302,101 teaches measurement of electroresistivity of a core sample maintained under constant pressure with power supplied by an alternating current and U.S. Pat. No. 4,686,477 teaches application of multi-frequency electric current to a sub-surface formation for ascertainment of the relation of resistivity versus frequency for characterization of rock lithology.
The methods taught by the prior art patents have many disadvantages. Neither the streaming potential nor the electro-osmotic measurement alone is a reliable indication of formation permeability, especially in formations of low permeability. Attempts to measure the streaming potential signal with electrodes at distances greater than one wavelength from each other are flawed since pressure oscillation propagates as a sound wave and the pressure difference would depend on both the magnitude and the phase of the wave and the streaming potential signal would be very low since considerable energy is lost to viscous dissipation over such a distance. Movement of the electrode in well fluid is disadvantageous since its own surface potential would be disturbed and oscillate at the same frequency causing an oscillating voltage much stronger than the streaming potential signal. Application of a d.c. flow to a formation and measurement of the response voltage in the time domain will not work in low permeability formations since the longer response time and very low streaming potential signal is dominated over by drifts of the electrodes' interfacial voltage over time. Measurement of a pressure signal resulting from the electro-osmotic effect would be even more difficult since it would be very weak and inseparable from the much larger voltage signal at the same frequency resulting from formation resistivity. Proposed measurement of the phase-shift in the frequency domain would be even more difficult than the suggested measurement of the response time in the time domain.